10 Summary and Discussion

In this review, after briefly presenting the currently favored CDM model of cosmology (which clearly
works overwhelmingly well on large scales despite its slightly unelegant mixture of currently unknown
elements, Sections 2 and 3), we reviewed the few most outstanding challenges that this model is still
facing (Section 4), which will have to be addressed one way or the other in the coming years.
These include coincidences at between the scale of the energy density in dark energy,
dark matter, and baryonic matter, as well as a common natural scale for the behavior of the
dark matter and dark energy sectors. What is more, as far as galaxy formation is concerned,
many predictions made by the model (keeping in mind that baryon physics could modify these
predictions) were ruled out by observations: these include many observations indicating that
structure formation should take place earlier than predicted, the low number of observed satellites
around the Milky Way (especially the missing satellites at the low and high mass ends of the
mass function), the phase-space correlation of satellite galaxies of the Milky Way as opposed to
their predicted isotropic distribution, the apparent presence of constant DM density cores in
the central parts of galaxies instead of the predicted cuspy dark halos, the over-abundance of
large bulgeless thin disk galaxies that are extremely difficult to produce in simulations, or the
presence of spiral arms in disks that should be immune to such instabilities. But even more
challenging is the appearance (Figure 48) of an acceleration constant (i.e., the
common scale of the dark matter and dark energy sectors as in natural units)
in many unrelated scaling relations for DM and baryons in galaxies. These scaling relations
involve a possibly devastating amount of fine-tuning for all collisionless dark matter models
(Section 4.3), and can all be summarized by Milgrom’s empirical formula (Section 5), meaning that the
observed gravitational field in galaxies is mimicking a universal force law generated by the baryons
alone.

Figure 48: The acceleration parameter of extragalactic systems, spanning ten
decades in baryonic mass . X-ray emitting galaxy groups and clusters are visibly offset from
smaller systems, but by a remarkably modest amount over such a long baseline. The characteristic
acceleration scale is in the data, irrespective of the interpretation. And it actually plays
various other independent roles in observed galaxy phenomenology. This is natural in MOND (see
Section 5.2), but not in CDM (see Section 4.3).

With inert, collisionless and dissipationless DM, making Milgrom’s law emerge requires a huge, and
perhaps even unreasonable, amount of fine-tuning in the expected feedback from the baryons. Indeed, the
relation between the distribution of baryons and DM should depend on the various different histories of
formation, intrinsic evolution, and interaction with the environment of the various different galaxies,
whereas Milgrom’s law provides a sucessful unique and history-independent relation. Given this puzzle, the
central idea of Modified Newtonian Dynamics (MOND) is rather to explore the possibility that the force
law is indeed effectively modified (Section 6). The main motivation for studying MOND is
thus a fully empiricist one, as it is driven by the observed phenomenology on galaxy scales,
and not by an aesthetic wish of getting rid of DM. The corollary is that it is not a problem
for a theory designed to reproduce the uncanny successes of the MOND phenomenology to
replace CDM by “dark fields” (see Section 7) or more exotic forms of DM, different from simple
collisionless DM particles, contrary to the common belief that this would be against the spirit of
the MOND paradigm (although it is true that it would be more elegant to avoid too many
additional degrees of freedom). It is perhaps more important that, if MOND is correct in the sense
of the acceleration being a truly fundamental quantity, the strong equivalence principle
cannot hold anymore, and local Lorentz invariance could perhaps be spontaneously violated
too.

At this juncture, it is worthwhile to summarize the general predictions of MOND, as a paradigm, and
their observational tests (Table 2). As a mathematical description of the effective force law, MOND works
remarkably well in individual galaxies. As a modified gravity theory (at the classical level), it makes some
predictions that are both unique and challenging to reproduce in the context of the CDM paradigm.
However, MOND faces sharp challenges, particularly with cosmology and in rich clusters of galaxies, which
will not be conclusively addressed without a viable parent theory (Section 7), based on first principles and
underlying the MOND paradigm (if such a theory exists at all). In any case, in his series of papers
introducing the idea in 1983, Milgrom [294] made a few very explicit predictions, which we quote hereafter,
and compare with modern observational data (see also the Kepler-like laws of galactic dynamics in
Section 5.2):

“Velocity curves calculated with the modified dynamics on the basis of the observed mass ingalaxies should agree with the observed curves.”

It is now well established that MOND provides good fits to the rotation curves of galaxies
(Figure 23[401, 166]), including bumps and wiggles associated with a baryonic counterpart
(Figure 21, Kepler-like law no. 10 in Section 5.2). These fits are obtained with a single free
parameter per galaxy, the mass-to-light ratio of the stars. What makes them most impressive
is that the best-fit mass-to-light ratios, obtained on purely dynamical grounds assuming
MOND, vary with galaxy color exactly as one would expect from stellar population synthesis
models [42], that are based on astronomers’ detailed understanding of stars. Note that the
rotation curves of galaxies are predicted to be asymptotically flat, even though this flatness is
not always attained at the last observed point (see Kepler-like law no. 1 in Section 5.2, and
last explicit prediction hereafter).

“The relation between the asymptotic velocity and the mass of the galaxy is an absolute one.”

This is the Baryonic Tully–Fisher relation with (see Kepler-like laws no. 2
in Section 5.2). It appears to hold quite generally [272], even for galaxies that we would
conventionally expect to deviate from it [165, 279, 276].

“Analysis of the-dynamics in disk galaxies using the modified dynamics should yield surfacedensities, which agree with the observed ones.”

This states that, in addition to the radial force giving the rotation curve, the motions of stars
perpendicular to the disk must also follow from the source baryons (see Section 6.5.3). This
proves to be a remarkably challenging observation, and such data for external galaxies are
difficult to obtain [44]. To make matters still more difficult, the radial acceleration usually
dominates the vertical (). This has the consequence that the distinction between
MOND and conventional dynamics is not pronounced in regions that are well observed,
becoming pronounced only at rather low baryonic surface densities [279]. The vertical velocity
dispersions in low surface density regions (see Section 6.5.3) is typically 8 km/s [25, 241].
This exceeds the nominal Newtonian expectation (typically 2 km/s for ,
depending on the thickness of the disk), and is more in accordance with MOND. However,
it would require a considerably more detailed analysis to consider this a test, let alone a
success, of MOND. The Milky Way (Section 6.5.2) may provide an excellent test for this
prediction [50, 378] as more precision data become available.

“Effects of the modification are predicted to be particularly strong in (LSB) dwarf galaxies.”

The dwarf spheroidal satellite galaxies of the Milky Way have very low surface densities of
stars, so (see Kepler-like law no. 8 in Section 5.2) are far into the MOND regime. As expected,
these systems exhibit large mass discrepancies [477, 427]. Detailed fits to the better observed
“classical” dwarfs [8] are satisfactory in most cases (see Section 6.6.2). The “ultrafaint” dwarfs
appear more problematic [285], in the sense that their velocity dispersions are higher than
expected. This might be an indication of the MOND-specific external field effect (see Section 6.3
and [78]), as the field of the Milky Way dominates the internal fields of the ultrafaint dwarfs.
If so, these objects are not in dynamical equilibrium, which considerably complicates their
analysis.

Locally-measured mass-to-light ratios should show no indication of hidden mass when, but rise beyond the radius where.

We have paraphrased this prediction for brevity (see also Kepler-like law no. 7 in Section 5.2).
The test of this prediction is shown in Figures 10, 11, and 14. The predicted effect is obvious in
the data with populations synthesis mass-to-light ratios for the stars [42], or with dynamical
mass-to-light ratios [279] that make no assumption about stellar mass. In HSB spirals, there is
no obvious need for dark matter in the inner regions, with the mass discrepancy only appearing
at large radii as the acceleration drops below (Figure 10).

Low surface brightness means low stellar surface density, which in turns means low acceleration.
LSB galaxies are thus predicted to be well into the modified regime (see also Kepler-like law
no. 8 in Section 5.2). This was a strong prediction, because few bona-fide examples of such
objects were known at the time. Indeed, in 1983, when these predictions were published, it
was widely thought that nearly all disk galaxies shared a common high surface brightness.
One specific consequence of MOND for LSB galaxies is that they should lie on the same
BTFR, with the same normalization, as HSB spirals. This was subsequently observed to be
the case [517, 443]. There is no systematic deviation from the BTFR with surface brightness
(Figure 5), thus contrary to what is naturally expected in conventional dynamics [279, 109].
Another consequence of low surface density is that the acceleration is low () everywhere.
As a result, the mass discrepancy appears at a smaller radius in LSB galaxies, and is larger in
amplitude than in HSB galaxies. This effect was subsequently observed (Figure 14[279]).

“We predict a correlation between the value of the average surface density of a galaxy and thesteepness with which the rotational velocity rises to its asymptotic value.”

MOND does not simply make rotation curves flat. It predicts that HSB galaxies have rotation
curves that rise rapidly before becoming flat, and may even fall towards asymptotic flatness. In
contrast, LSB galaxies should have slowly rising rotation curves that only gradually approach
asymptotic flatness (see also Kepler-like law no. 8 in Section 5.2). Both morphologies are
observed (Figure 15). The expected connection between dynamical acceleration and the surface
density of the source baryons is illustrated in Figures 9 and 16.

The original predictions listed above cover many situations, but not all. Indeed, once one writes a
specific force law, its application must be completely general. Such a hypothesis is readily subject to
falsification, provided sufficiently accurate data to test it – a perpetual challenge for astronomy. Table 2
summarizes the tests discussed here. By and large, tests of MOND involving rotationally-supported disk
galaxies are quite positive, as largely detailed above (see Section 6.5). By construction, there is no cusp
problem (solution to challenge no. 6 of Section 4.2), and no missing baryons problem (solution to challenge
no. 10 of Section 4.2), as the way the dynamical mass-to-light ratio systematically varies with the circular
velocity is a direct consequence of Milgrom’s law (Kepler-like law no. 4 of Section 5.2). There does
appear to be a relation between the quality of the data and the ease with which a MOND
fit to the rotation curve is obtained, in the sense that fits are most readily obtained with the
best data [28]. As the quality of the data decline [384], one begins to notice small disparities.
These are sometimes attributable to external disturbances that invalidate the assumption of
equilibrium [403]. For targets that are intrinsically difficult to observe, minor problems become
more common [120, 448]. These typically have to do with the challenges inherent in combining
disparate astronomical data sets (e.g., rotation curves measured independently at optical and radio
wavelengths) and constraining the inclinations of LSB galaxies (bear in mind that all velocities require
a correction to project the observed velocity into the plane of the disk, and mass in
MOND scales as the fourth power of velocity). Given the intrinsic difficulties of astronomical
observations, it is remarkable that the success rate of MOND fits is as high as it is: of the 78
galaxies that have been studied in detail (see Section 6.5.1), only a few cases (most notably
NGC 3198 [68, 166]) appear to pose challenges. Given the predictive and quantitative success of the
majority of the fits, it would seem unwise to ignore the forest and focus only on the outlying
trees.

One rotationally-supported system that is very familiar to us is the solar system (see Section 6.4). The
solar system is many orders of magnitude removed from the MOND regime (Figure 11), so no strong effects
are predicted. However, it is, of course, possible to obtain exquisitely precise data in the solar system, so it
is conceivable that some subtle effect may be observable [391]. Indeed, the lack of such effects on the inner
planets already appears to exclude some slowly-varying interpolation functions [62]. Other tests may yet
prove possible [37, 314], but, as they are strong-field gravity tests by nature, they all depend strongly
on the parent relativistic theory (Section 7) and how it converges towards GR [22]. So, in
Table 2, we list the status of solar-system tests as unclear, depending on the parent relativistic
theory.

An important aspect of galactic disks is their stability (see Section 6.5.3). Indeed, the need to stabilize
disks was one of the early motivations for invoking dark matter [343]. MOND appears able to provide the
requisite stability [77]. Indeed, it gives good reason [299] for the observed maximum in the distribution of
disk galaxy surface densities at (Freeman’s limit: Figure 8 and Kepler-like law no. 6 in
Section 5.2). Disks with surface densities below this threshold are in the low acceleration limit and can be
stabilized by MOND. Higher-surface-density disks would be purely in the Newtonian regime and subject to
the usual instabilities. Going beyond the amount of stability required for existence, another
positive aspect of MOND is that it does not over-stabilize disks. Features like bars and spiral
arms are a natural result of disk self-gravity. Conventionally, large halo-to-disk mass ratios
suppress the growth of such features, especially in LSB galaxies [291]. Yet such features are
present70.
The suppression is not as great in MOND [77], and numerical simulations appear to do a good job of
reproducing the range of observed morphologies of spiral galaxies (solution to challenge no. 9 of
Section 4.2, see [458]). Bars tend to appear more quickly and are fast, while warps can also be naturally
produced (Section 6.5.3). There appears to be no reason why this should not extend to thin and bulgeless
disks, whose ubiquity poses a challenge to galaxy formation models in CDM. This particular point of
creating large bulgeless disks (challenge no. 8 of Section 4.2) can actually be solved thanks to early
structure formation followed by a low galaxy-interaction rate in MONDian cosmology (see Section 9.2),
but this definitely warrants further investigation, so we mark this case as merely promising in
Table 2.

Interacting galaxies are, by definition, non-stationary systems in which the customary assumption of
equilibrium does not generally hold. This renders direct tests of MOND difficult. However, it is worth
investigating whether commonly observed morphologies (e.g., tidal tails) are even possible in MOND.
Initially, this seemed to pose a fundamental difficulty [279], as dark matter halos play a critical role in
absorbing the orbital energy and angular momentum that it is necessary to shed if passing galaxies are to
not only collide, but stick and merge. Nevertheless, recent numerical simulations appear to do a nice job of
reproducing observed morphologies [459]. This is no trivial feat. While it is well established that dark
matter models can result in nice tidal tails, it turns out to be difficult to simultaneously match the
narrow morphology of many observed tidal tails with rotation curves of the systems from which
they come [130]. Narrow tidal tails appear to be natural in MOND, as well as more extended
resulting galaxies, thanks to the absence of angular momentum transfer to the dark halo (solution
to challenge no. 7 of Section 4.2). Additionally, tidal dwarfs that form in these tails clearly
have characteristics closer to those observed (see Section 6.5.4) than those from dark matter
simulations [165, 309].

Spheroidal systems also provide tests of MOND (Section 6.6). Unlike the case of disk galaxies, where
orbits are coplanar and nearly circular so that the centripetal acceleration can be equated with the
gravitational force, the orbits in spheroidal systems are generally eccentric and randomly oriented. This
introduces an unknown geometrical factor usually subsumed into a parameter that characterizes the
anisotropy of the orbits. Accepting this, MOND appears to perform well in the classical dwarf spheroidal
galaxies, but implies that the ultrafaint dwarfs are out of equilibrium (see Section 6.6.2). For small systems
like the ultrafaint dwarfs and star clusters (Section 6.6.3) within the Milky Way, the external field
effect (Section 6.3) can be quite important. This means that star clusters generally exhibit
Newtonian behavior by virtue of being embedded in the larger galaxy. Deviations from purely
Newtonian behavior are predicted to be subtle and are fodder for considerable debate [199, 397],
rendering the present status unclear (Table 2). At the opposite extreme of giant elliptical galaxies
(Section 6.6.1), the data accord well with MOND [323]. Indeed, bright elliptical galaxies are
sufficiently dense that their inner regions are well into the Newtonian regime. In the MONDian
context, this is the reason that it has historically been difficult to find clear evidence for mass
discrepancies in these systems. The apparent need for dark matter does not occur until radii where
the accelerations become low. That only spheroidal stellar systems appear to exist at surface
densities in excess of is the corollary of Freeman’s limit: such dense systems could not
exist as stable disks, so must perforce become elliptical galaxies, regardless of the formation
mechanism that made them so dense. That populations of elliptical galaxies should obey the
Faber–Jackson relation (Kepler-like law no. 3 in Section 5.2, Figure 7) is also very natural to
MOND [383, 395].

The largest gravitationally-bound systems are also spheroidal systems: rich clusters of galaxies. The
situation here is quite problematic for MOND (Section 6.6.4). Applying MOND to ascertain the dynamical
mass routinely exceeds the observed baryonic mass by a factor of 2 to 3. In effect, MOND requires
additional dark matter in galaxy clusters. The need to invoke unseen mass is most unpleasant for a theory
that otherwise appears to be a viable alternative to the existence of unseen mass. However,
one should remember that the present-day motivation for studying MOND is driven by the
observed phenomenology on galaxy scales, summarized above, and not by an aesthetic wish
of getting rid of DM. What is more, parent relativistic theories of MOND might well involve
additional degrees of freedom in the form of “dark fields”. But in any case, one must be careful not
to conflate the rather limited missing mass problem that MOND suffers in clusters with the
non-baryonic collisionless cold dark matter required by cosmology. There is really nothing about
the cluster data that requires the excess mass to be non-baryonic, as long as it behaves in a
collisionless way. There could for instance be baryonic mass in some compact non-luminous form (see
Section 6.6.4 for an extensive discussion). This might seem to us unlikely, but it does have historical
precedent. When Zwicky [518] first identified the dark matter problem in clusters, the mass
discrepancy was of order 100. That is, unseen mass outweighed the visible stars by two orders of
magnitude. It was only decades later that it was recognized that baryons residing in a hot
intracluster gas greatly outweighed those in stars. In effect, there were [at least] two missing mass
problems in clusters. One was the hot gas, which reduces the conventional discrepancy from a
factor of 100 to a factor of 8 [175] in Newtonian gravity. From this perspective, the
remaining factor of two in MOND seems modest. Rich clusters of galaxies are rare objects, so the
total required mass density can readily be accommodated within the baryon budget of BBN.
Indeed, according to BBN, there must still be a lot of unidentified baryons lurking somewhere
in the universe. But the excess dark mass in clusters need not be baryonic, even in MOND.
Massive ordinary neutrinos [389, 392] and light sterile neutrinos [9, 13] have been suggested as
possible forms of dark matter that might provide an explanation for the missing mass in clusters.
Both are non-baryonic, but as they are hot DM particle candidates, neither can constitute the
cosmological non-baryonic cold dark matter. At this juncture, all we can say for certain is that we
do not know what the composition of the unseen mass is. It could even just be evidence for
the effect of additional “dark fields” in the parent relativistic formulation of MOND, such as
massive scalar fields, vector fields, dipolar dark matter, or even subtle non-local effects (see
Section 7).

There are other aspects of cluster observations that are more in line with MOND’s predictions. Clusters
obey a mass–temperature relation that parallels the prediction of MOND
(Figures 39 and 48) more closely than the conventional prediction of expectation in
CDM, without the need to invoke preheating (a need that may arise as an artifact of the
mismatch in slopes). Indeed, Figure 48 shows clearly both the failing of MOND in the offset in
characteristic acceleration between clusters and lower mass systems, and its successful prediction
of the slope (a horizontal line in this figure). A further test, which may be important is the
peculiar and bulk velocity of clusters. For example, the collision velocity of the bullet cluster is so
large71
as to be highly improbable in CDM (occurring with a probability of [249]). In contrast, large
collision velocities are natural to MOND [16]. Similarly, the large scale peculiar velocity of
clusters is observed to be [221], well in excess of the expected .
Ongoing simulations with MOND [11] show some promise to produce large peculiar velocities for
clusters. In general, one would expect high speed collisions to be more ubiquitous in MOND than
CDM.

An important line of evidence for mass discrepancies in the universe is gravitational lensing in excess of
that expected from the observed mass of lens systems. Lensing is an intrinsically relativistic effect that
requires a generally covariant theory to properly address. This necessarily goes beyond MOND
itself into specific hypotheses for its parent theory (Section 7), so is somewhat different than
the tests discussed above. Broadly speaking, tests involving strong gravitational lensing fare
tolerably well (Section 8.1), whereas weak lensing tests, that are sensitive to larger-scale mass
distributions, are more problematic (Sections 8.2, 8.3, and 8.4) or simply crash into the usual missing
mass problem of MOND in clusters. Note that weak lensing in relativistic MOND theories
produces the same amount of lensing as required from dynamics, so this is not the problem. The
problematic fact is just that some tests seem to require more dark matter than the effect of MOND
provides.

On larger (cosmological) scales, MOND, as a modification of classical (non-covariant) dynamics, is
simply unsatisfactory or mute. MOND itself has no cosmology, providing analogs for neither the
Friedmann equation for the dynamics of the universe, nor the Robertson–Walker metric for its
geometry. For these, one must appeal to specific hypotheses for the relativistic parent theory
of MOND (Section 7), which is far from unique, and theoretically not really satisfactory, as
none of the present candidates emerges from first principles. At this juncture, it is not clear
whether a compelling candidate cosmology will ever emerge. But on the other hand, there is
nothing about MOND as a paradigm that contradicts per se the empirical pillars of the hot big
bang: Hubble expansion, BBN, and the relic radiation field (Section 9). The formation of large
scale structure is one of the strengths of conventional theory, which can be approached with
linear perturbation theory. This leads to good fits of the power spectrum, both at early times
( in the cosmic microwave background) and at late times (the galaxy power
spectrum [452]). In contrast, the formation of structure in MOND is intrinsically non-linear.
Therefore, it is unclear whether MOND-motivated relativistic theories will inevitably match the
observed galaxy power spectrum, a possible problem being how to damp the baryon acoustic
oscillations [127, 430]. At this stage, a unique prediction does not exist. Nevertheless, there are two aspects
of structure formation in MOND that appear to be fairly generic and distinct from CDM.
The stronger effective long range force in MOND speeds the growth rate, but has less mass to
operate with as a source. Consequently, radiation domination persists longer and structure
formation is initially inhibited (at redshifts of hundreds). Once structure begins to form, the
non-linearity of MOND causes it to proceed more rapidly than in GR with CDM. Three observable
consequences would be (i) the earlier emergence of large objects like galaxies and clusters in the cosmic
web (as well as the associated low interaction rate at smaller redshifts) providing a possible
solution to challenge no. 2 of Section 4.2[11], (ii) the more efficient evacuation of large voids
(possible solution to challenge no. 3 of Section 4.2), and (iii) larger peculiar (and collisional [16])
velocities of galaxy clusters (solution to challenge no. 1 of Section 4.2). However, the potential
downside to rapid structure formation in MOND is that it may overproduce structure by redshift
zero [341, 250].

The final entries in Table 2 regard the cosmic microwave background, discussed in more detail in
Section 9.2. The third peak of the acoustic power spectrum of the CMB poses perhaps the most severe
challenge to a MONDian interpretation of cosmology. The amplitude of the third peak measured by WMAP
is larger than expected in a universe composed solely of baryons [442]. This implies some substance that
does not oscillate with the baryons. Cold dark matter fits this bill nicely. In the context of MOND, we must
invoke some other massive substance (i.e., non-baryonic dark matter such as, e.g., light sterile neutrinos [9])
that plays the role of CDM, or rely on additional degrees of freedom in the relativistic parent theory of
MOND (see Section 7) that would have the same net result (see the extensive discussion in Section 9.2), or
even combine non-baryonic dark matter with these additional degrees of freedom [430]. While these are
real possibilities, neither are particularly appealing, any more than it is to invoke CDM with
complex fine-tuned feedback to explain rotation curves that apparently require only baryons as a
source.

The missing baryon problem that MOND suffers in rich clusters of galaxies and the third peak of the
acoustic power spectrum of the CMB are thus the most serious challenges presently facing MOND. But
even so, the interpretation of the acoustic power spectrum is not entirely clear cut. Though there is no
detailed fit to the power spectrum in MOND (unless we invoke 10 eV-scale sterile neutrinos [9]), MOND
did motivate the prediction [265] of two aspects of the CMB that were surprising in CDM (see
Section 9.2). The amplitude ratio of the first-to-second peak in the acoustic power spectrum was outside
the bounds expected ahead of time by CDM for from BBN as it was then known (see Section 9.2).
In contrast, the first:second acoustic peak ratio that is now well measured agrees well with the
quantitative value predicted in advance for the case of the absence of cold dark matter [268, 269].
Similarly, the rapid formation of structure expected in MOND leads naturally to an earlier epoch of
re-ionization than had been anticipated in CDM [265, 269]. Thus, while the amplitude of the third
peak is clearly problematic and poses a severe challenge to any MOND-inspired theories, the
overall interpretation of the CMB is debatable. While the existence of non-baryonic cold dark
matter is the most obvious explanation of the third peak indeed, it is not at all obvious that
straightforward CDM – in the form of rather simple massive inert collisionless particles – is uniquely
required.

Science is, in principle, about theories or models that are falsifiable, and thus that are presently either
falsified or not. But in practice it does not (and cannot) really work that way: if a model that was making
good predictions up to a certain point suddenly does not work anymore (i.e., does not fit some new data),
one obviously first tries to adjust it to make it fit the observations rather than throwing it away
immediately. This is what one calls the requisite “compensatory adjustments” of the theory (or of the
model): Popper himself drew attention to these limitations of falsification in The Logic of ScientificDiscovery[355]. In the case of the CDM model of cosmology, which is mostly valid on large scales, the
current main trend is to find the “compensatory adjustments” to the model to make it fit in galaxies,
mainly by changing (or mixing) the mass(es) of the dark matter particles, and/or through
artificially fine-tuned baryonic feedback in order to reproduce the success of MOND. Incidentally,
exactly the same is true for MOND, but for the opposite scales: MOND works remarkably well in
galaxies but apparently needs compensatory adjustments on larger scales to effectively replace
CDM. Now does that mean that falsification is impossible? That all models are equal? Surely
not. In the end, a theory or a model is really falsified once there are too many compensatory
adjustments (needed in order to fit too many discrepant data), or once these become too twisted
(like Tycho Brahe’s geocentric model for the solar system). But there is obviously no truly
quantitative way of ascertaining such global falsification. How one chooses to weigh the evidence
presented in this review necessarily informs one’s opinion of the relative merits of CDM and
MOND. If one is most familiar with cosmology and large scale structure, CDM is the obvious
choice, and it must seem rather odd that anyone would consider an alternative as peculiar as
MOND, needing rather bizarre adjustments to match observations on large scales. But if one is
more concerned with precision dynamics and the observed phenomenology in a wide swath of
galaxy data, it seems just as strange to invoke non-baryonic cold dark matter together with
fine-tuned feedback to explain the appearance of a single effective force law that appears to act with
only the observed baryons as a source. Perhaps the most important aspect before one throws
away any model is to have a “simpler” model at hand, that still reproduces the successes of
the earlier favored model but also naturally explains the discrepant data. In that sense, right
now, it is absolutely fair to say that there is no alternative, which really does better overall
than CDM, and in favor of which Ockham’s razor would be. However, it would probably
be a mistake to persistently ignore the fine-tuning problems for dark matter and the related
uncanny successes of the MOND paradigm on galaxy scales, as they could very plausibly point
at a hypothetical better new theory. It is also important to bear in mind that MOND, as a
paradigm or as a modification of Newtonian dynamics, is not itself generally covariant. Attempts to
construct relativistic theories that contain MOND in the appropriate limit (Section 7) are
correlated but distinct efforts, and one must be careful not to conflate the two. For example,
some theories, like TeVeS (Section 7.4), might make predictions that are distinct from GR
in the strong-field regime. Should future tests falsify these distinctive predictions of TeVeS
while confirming those of GR, this would perhaps falsify TeVeS as a viable parent theory for
MOND, but would have no bearing on the MONDian phenomenology observed in the weak-field
regime, nor indeed on the viability of MOND itself. It would perhaps simply indicate the need
to continue to search for a deeper theory. It would, for instance, be extremely alluring if one
could manage to find a physical connection between the dark energy sector and the possible
breakdown of standard dynamics in the weak-field limit, since both phenomena would then
simply reflect discrepancies with the predictions of GR when is set to zero (see, e.g.,
Section 7.10). Of course, it is perfectly conceivable that such a deep theory does not exist, and that
the apparent MONDian behavior of galaxies will be explained through small compensatory
adjustments of the current CDM paradigm, but one has yet to demonstrate how this will
occur, and it will inevitably involve a substantial amount of fine-tuning that will have to be
explained naturally. In any case, the existence of a characteristic acceleration (Figure 48)
playing various different roles in many seemingly-independent galactic scaling relations (see
Sections 4.3 and 5.2) is by now an empirically established fact, and it is thus mandatory for any
successful model of galaxy formation and evolution to explain it. The future of this field of
research might thus still be full of exciting surprises for astronomers, cosmologists, and theoretical
physicists.